On turn 13, I applied the dogma of Machine Tools - Draw and score a card equal in value to the highest card in your score pile. The highest in my pile was a 2, and he had nothing scored. We had an equal number of red factory icons, so the effect was shared, but I would take that to be he has nothing in his score pile so draws and scores nothing. Instead, he drew and scored a 2. It looks like it applied the "your" clause to my score pile even for his sharing.

If you have nothing in your score pile, the value of the highest card in your score pile is treated as 0. This means he tried to score a 0 but there were none, so he tried a 1. Presumably that pile was empty too so he scored a 2.